Unbeknownst to many, there are two ways of tying your shoelace. You see, the first step is usually like this.
In the second step, you can
either
do it like this,
in which case,
you see, the knot becomes kind of perpendicular to the direction of the lace at the end.
Or, you can do exactly the mirror image of what you have just done.
And it is slightly wrong, actually, when you do this.
But that's a nice way to do it.
When you do that,
in this case, the knot becomes kind of parallel, if you see what I mean, to the shoelace.
What did I do? So, there are two ways of doing it, right? You can do, start from, like, this,
or the other direction. So let's do it in this direction, in some sense.
Now, that determines one of the orientations.
So, one way to do it is to, from my point of view, the right hand, and pull it over, and then do this,
which produces a
perpendicular knot.
The other way is
to make the loop with my
left hand, and then turn it over and through, and then make the knot, in which case
the knot becomes parallel to the shoelace. That's quite interesting. Now, it turns out that these two things have a difference.
And I'd like to show one of the differences. Which is also a nice trick to know in practice, in daily life. Let's make a knot
by first doing this, and then, secondly,
by doing that. If you think of this as a mirror, this is not
symmetric with respect to this mirror. Because you see, this strand goes under this loop, whereas this one goes over this loop.
It's kind of more like a, you know,
rotation symmetry. Whereas if I put them in this configuration, that's symmetric, in the sense that they're both going under.
And you can see that it is symmetric. Now,
Brady: "So which one matches which shoelace?"
I think this one matches the parallel one, and the rotation one matches the perpendicular one.
I'm not entirely sure about this. You explore. Okay.
So, let's make a tight knot with this. And this is a fairly tight knot. This was the symmetric one.
And, you know, if you wanted to undo this knot, you have to go in, and it's really a bothersome.
But there is actually a nice trick to undo this knot.
Let me show it to you first. I hold it like this. It comes straight off.
What did I do?
Let's do it in slow motion and in detail. Again, this is the symmetric one. And when I
close it, it's like that.
You grab those two or those two. It doesn't matter which one, let's. And when you pull them taut,
you get the straight line.
And it turns out that the knot, the entire knot, can slide across the, along the straight line.
And it just comes off the end
and undoes itself.
So this kind of symmetric knot is quite fragile.
Or, if you like, if you knotted it like this, as far as it's somewhere in the middle,
it's quite tight, and it's, it's secure. But if you want to untie it,
you don't have to go in and mess around with just undoing that, I need to, a little bit.
You can pull it off, slide it off completely. Whereas, if you made the other
rotational knot, which one is it? It's I think this one.
Brady: "This is a the asymmetric."
Asymmetric one. And this one goes over, this one goes under. It's not symmetric with respect to the similar.
That's a very secure knot. You can't really undo it. The only way to undo it is to actually go in.
So it's useful to know, by the way.
You know, what is this thing? It certainly has a lot of crossings. But again
we're looking for the minimal number of crossings, so we try to untangle this and open it up as much as we possibly can.
And if you're patient enough and do that